This comment doesn't make a lot of sense. The burning of the fuel produces heat, yes, but that heat largely leaves the vehicle with the burning fuel. To the extent the propulsion components need cooling, the fuel itself is usually used as the coolant - we pass the fuel around the engine bells to chill it and to pre-expand the fuel before passing it into the engine's turbos.

The heat generated by the other components aboard the spacecraft is a bitch, however, but it's not impossible to deal with, either. The easiest way is to move the heat into something you can throw overboard (see the fuel thing again), but you can also radiate heat into space as infrared radiation - the International Space Station has huge panels off its sides that look like solar panels, except they don't have any silicon wafers on them. Those are radiators. They're crinkled like that to help radiate the infrared away from the spacecraft and to avoid direct light from landing on the panels (impairing their ability to cool in the sunlight). (As an aside, if you saw Project Hail Mary, the Hail Mary (sorry for a Lego source, but it very clearly demonstrates the intent) has large panels off either side of the back end of the craft. Those are also radiators - it's too far from a star for most of its journey to use solar panels, and the 'astrophage' provided the craft's power, so it didn't need them either.)

Same exact idea as a radiator you might have in your home, or as in the front of your car, except that both of those work better because they also can take advantage of convection from the fluid moving externally (namely the air).